Reflection of a spherical wave by acoustically hard, concave cylindrical walls based on the tangential plane approximation.

The tangential plane approximation (TPA) is introduced to investigate the spherical wave reflection from smooth concave cylindrical walls, and as a practical calculation scheme, asymptotic expression of the reflected sound from that surface with a relatively large dimension is derived. The physical condition under which TPA holds is derived for the spherical wave incidence; moreover, the essential properties of the reflected sound from the curved walls, which cannot be treated by the geometrical acoustics, are discussed through the numerical calculation for infinitely long cylinders. A formula of the reflection factor of the two-dimensional curved surface is obtained for the purpose of the room acoustical design. This formula coincides with that based on the geometrical acoustics when the frequency is infinitely high. [ABSTRACT FROM AUTHOR]